A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Computational methods and software systems for dynamics and control of large space structures

Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers

Parallel Architectures for Planetary Exploration Requirements (PAPER)

The Parallel Architectures for Planetary Exploration Requirements (PAPER) project is essentially research oriented towards technology insertion issues for NASA's unmanned planetary probes. It was initiated to complement and augment the long-term efforts for space exploration with particular reference to NASA/LaRC's (NASA Langley Research Center) research needs for planetary exploration missions of the mid and late 1990s. The requirements for space missions as given in the somewhat dated Advanced Information Processing Systems (AIPS) requirements document are contrasted with the new requirements from JPL/Caltech involving sensor data capture and scene analysis. It is shown that more stringent requirements have arisen as a result of technological advancements. Two possible architectures, the AIPS Proof of Concept (POC) configuration and the MAX Fault-tolerant dataflow multiprocessor, were evaluated. The main observation was that the AIPS design is biased towards fault tolerance and may not be an ideal architecture for planetary and deep space probes due to high cost and complexity. The MAX concepts appears to be a promising candidate, except that more detailed information is required. The feasibility for adding neural computation capability to this architecture needs to be studied. Key impact issues for architectural design of computing systems meant for planetary missions were also identified

Scalability of broadcast performance in wireless network-on-chip

Networks-on-Chip (NoCs) are currently the paradigm of choice to interconnect the cores of a chip multiprocessor. However, conventional NoCs may not suffice to fulfill the on-chip communication requirements of processors with hundreds or thousands of cores. The main reason is that the performance of such networks drops as the number of cores grows, especially in the presence of multicast and broadcast traffic. This not only limits the scalability of current multiprocessor architectures, but also sets a performance wall that prevents the development of architectures that generate moderate-to-high levels of multicast. In this paper, a Wireless Network-on-Chip (WNoC) where all cores share a single broadband channel is presented. Such design is conceived to provide low latency and ordered delivery for multicast/broadcast traffic, in an attempt to complement a wireline NoC that will transport the rest of communication flows. To assess the feasibility of this approach, the network performance of WNoC is analyzed as a function of the system size and the channel capacity, and then compared to that of wireline NoCs with embedded multicast support. Based on this evaluation, preliminary results on the potential performance of the proposed hybrid scheme are provided, together with guidelines for the design of MAC protocols for WNoC.Peer ReviewedPostprint (published version

Design and resource management of reconfigurable multiprocessors for data-parallel applications

FPGA (Field-Programmable Gate Array)-based custom reconfigurable computing machines have established themselves as low-cost and low-risk alternatives to ASIC (Application-Specific Integrated Circuit) implementations and general-purpose microprocessors in accelerating a wide range of computation-intensive applications. Most often they are Application Specific Programmable Circuiits (ASPCs), which are developer programmable instead of user programmable. The major disadvantages of ASPCs are minimal programmability, and significant time and energy overheads caused by required hardware reconfiguration when the problem size outnumbers the available reconfigurable resources; these problems are expected to become more serious with increases in the FPGA chip size. On the other hand, dominant high-performance computing systems, such as PC clusters and SMPs (Symmetric Multiprocessors), suffer from high communication latencies and/or scalability problems. This research introduces low-cost, user-programmable and reconfigurable MultiProcessor-on-a-Programmable-Chip (MPoPC) systems for high-performance, low-cost computing. It also proposes a relevant resource management framework that deals with performance, power consumption and energy issues. These semi-customized systems reduce significantly runtime device reconfiguration by employing userprogrammable processing elements that are reusable for different tasks in large, complex applications. For the sake of illustration, two different types of MPoPCs with hardware FPUs (floating-point units) are designed and implemented for credible performance evaluation and modeling: the coarse-grain MIMD (Multiple-Instruction, Multiple-Data) CG-MPoPC machine based on a processor IP (Intellectual Property) core and the mixed-mode (MIMD, SIMD or M-SIMD) variant-grain HERA (HEterogeneous Reconfigurable Architecture) machine. In addition to alleviating the above difficulties, MPoPCs can offer several performance and energy advantages to our data-parallel applications when compared to ASPCs; they are simpler and more scalable, and have less verification time and cost. Various common computation-intensive benchmark algorithms, such as matrix-matrix multiplication (MMM) and LU factorization, are studied and their parallel solutions are shown for the two MPoPCs. The performance is evaluated with large sparse real-world matrices primarily from power engineering. We expect even further performance gains on MPoPCs in the near future by employing ever improving FPGAs. The innovative nature of this work has the potential to guide research in this arising field of high-performance, low-cost reconfigurable computing. The largest advantage of reconfigurable logic lies in its large degree of hardware customization and reconfiguration which allows reusing the resources to match the computation and communication needs of applications. Therefore, a major effort in the presented design methodology for mixed-mode MPoPCs, like HERA, is devoted to effective resource management. A two-phase approach is applied. A mixed-mode weighted Task Flow Graph (w-TFG) is first constructed for any given application, where tasks are classified according to their most appropriate computing mode (e.g., SIMD or MIMD). At compile time, an architecture is customized and synthesized for the TFG using an Integer Linear Programming (ILP) formulation and a parameterized hardware component library. Various run-time scheduling schemes with different performanceenergy objectives are proposed. A system-level energy model for HERA, which is based on low-level implementation data and run-time statistics, is proposed to guide performance-energy trade-off decisions. A parallel power flow analysis technique based on Newton\u27s method is proposed and employed to verify the methodology

Principles for problem aggregation and assignment in medium scale multiprocessors

One of the most important issues in parallel processing is the mapping of workload to processors. This paper considers a large class of problems having a high degree of potential fine grained parallelism, and execution requirements that are either not predictable, or are too costly to predict. The main issues in mapping such a problem onto medium scale multiprocessors are those of aggregation and assignment. We study a method of parameterized aggregation that makes few assumptions about the workload. The mapping of aggregate units of work onto processors is uniform, and exploits locality of workload intensity to balance the unknown workload. In general, a finer aggregate granularity leads to a better balance at the price of increased communication/synchronization costs; the aggregation parameters can be adjusted to find a reasonable granularity. The effectiveness of this scheme is demonstrated on three model problems: an adaptive one-dimensional fluid dynamics problem with message passing, a sparse triangular linear system solver on both a shared memory and a message-passing machine, and a two-dimensional time-driven battlefield simulation employing message passing. Using the model problems, the tradeoffs are studied between balanced workload and the communication/synchronization costs. Finally, an analytical model is used to explain why the method balances workload and minimizes the variance in system behavior

Using Imprecise Computing for Improved Real-Time Scheduling

Conventional hard real-time scheduling is often overly pessimistic due to the worst case execution time estimation. The pessimism can be mitigated by exploiting imprecise computing in applications where occasional small errors are acceptable. This leverage is investigated in a few previous works, which are restricted to preemptive cases. We study how to make use of imprecise computing in uniprocessor non-preemptive real-time scheduling, which is known to be more difficult than its preemptive counterpart. Several heuristic algorithms are developed for periodic tasks with independent or cumulative errors due to imprecision. Simulation results show that the proposed techniques can significantly improve task schedulability and achieve desired accuracy– schedulability tradeoff. The benefit of considering imprecise computing is further confirmed by a prototyping implementation in Linux system. Mixed-criticality system is a popular model for reducing pessimism in real-time scheduling while providing guarantee for critical tasks in presence of unexpected overrun. However, it is controversial due to some drawbacks. First, all low-criticality tasks are dropped in high-criticality mode, although they are still needed. Second, a single high-criticality job overrun leads to the pessimistic high-criticality mode for all high-criticality tasks and consequently resource utilization becomes inefficient. We attempt to tackle aforementioned two limitations of mixed-criticality system simultaneously in multiprocessor scheduling, while those two issues are mostly focused on uniprocessor scheduling in several recent works. We study how to achieve graceful degradation of low-criticality tasks by continuing their executions with imprecise computing or even precise computing if there is sufficient utilization slack. Schedulability conditions under this Variable-Precision Mixed-Criticality (VPMC) system model are investigated for partitioned scheduling and global fpEDF-VD scheduling. And a deferred switching protocol is introduced so that the chance of switching to high-criticality mode is significantly reduced. Moreover, we develop a precision optimization approach that maximizes precise computing of low-criticality tasks through 0-1 knapsack formulation. Experiments are performed through both software simulations and Linux proto- typing with consideration of overhead. Schedulability of the proposed methods is studied so that the Quality-of-Service for low-criticality tasks is improved with guarantee of satisfying all deadline constraints. The proposed precision optimization can largely reduce computing errors compared to constantly executing low-criticality tasks with imprecise computing in high-criticality mode

Novel Cache Hierarchies with Photonic Interconnects for Chip Multiprocessors

[ES] Los procesadores multinúcleo actuales cuentan con recursos compartidos entre los diferentes núcleos. Dos de estos recursos compartidos, la cache de último nivel y el ancho de banda de memoria principal, pueden convertirse en cuellos de botella para el rendimiento. Además, con el crecimiento del número de núcleos que implementan los diseños más recientes, la red dentro del chip también se convierte en un cuello de botella que puede afectar negativamente al rendimiento, ya que las redes tradicionales pueden encontrar limitaciones a su escalabilidad en el futuro cercano. Prácticamente la totalidad de los diseños actuales implementan jerarquías de memoria que se comunican mediante rápidas redes de interconexión. Esta organización es eficaz dado que permite reducir el número de accesos que se realizan a memoria principal y la latencia media de acceso a memoria. Las caches, la red de interconexión y la memoria principal, conjuntamente con otras técnicas conocidas como la prebúsqueda, permiten reducir las enormes latencias de acceso a memoria principal, limitando así el impacto negativo ocasionado por la diferencia de rendimiento existente entre los núcleos de cómputo y la memoria. Sin embargo, compartir los recursos mencionados es fuente de diferentes problemas y retos, siendo uno de los principales el manejo de la interferencia entre aplicaciones. Hacer un uso eficiente de la jerarquía de memoria y las caches, así como contar con una red de interconexión apropiada, es necesario para sostener el crecimiento del rendimiento en los diseños tanto actuales como futuros. Esta tesis analiza y estudia los principales problemas e inconvenientes observados en estos dos recursos: la cache de último nivel y la red dentro del chip. En primer lugar, se estudia la escalabilidad de las tradicionales redes dentro del chip con topología de malla, así como esta puede verse comprometida en próximos diseños que cuenten con mayor número de núcleos. Los resultados de este estudio muestran que, a mayor número de núcleos, el impacto negativo de la distancia entre núcleos en la latencia puede afectar seriamente al rendimiento del procesador. Como solución a este problema, en esta tesis proponemos una de red de interconexión óptica modelada en un entorno de simulación detallado, que supone una solución viable a los problemas de escalabilidad observados en los diseños tradicionales. A continuación, esta tesis dedica un esfuerzo importante a identificar y proponer soluciones a los principales problemas de diseño de las jerarquías de memoria actuales como son, por ejemplo, el sobredimensionado del espacio de cache privado, la existencia de réplicas de datos y rigidez e incapacidad de adaptación de las estructuras de cache. Aunque bien conocidos, estos problemas y sus efectos adversos en el rendimiento pueden ser evitados en procesadores de alto rendimiento gracias a la enorme capacidad de la cache de último nivel que este tipo de procesadores típicamente implementan. Sin embargo, en procesadores de bajo consumo, no existe la posibilidad de contar con tales capacidades y hacer un uso eficiente del espacio disponible es crítico para mantener el rendimiento. Como solución a estos problemas en procesadores de bajo consumo, proponemos una novedosa organización de jerarquía de dos niveles cache que utiliza una red de interconexión óptica. Los resultados obtenidos muestran que, comparado con diseños convencionales, el consumo de energía estática en la arquitectura propuesta es un 60% menor, pese a que los resultados de rendimiento presentan valores similares. Por último, hemos extendido la arquitectura propuesta para dar soporte tanto a aplicaciones paralelas como secuenciales. Los resultados obtenidos con la esta nueva arquitectura muestran un ahorro de hasta el 78 % de energía estática en la ejecución de aplicaciones paralelas.[CA] Els processadors multinucli actuals compten amb recursos compartits entre els diferents nuclis. Dos d'aquests recursos compartits, la memòria d’últim nivell i l'ample de banda de memòria principal, poden convertir-se en colls d'ampolla per al rendiment. A mes, amb el creixement del nombre de nuclis que implementen els dissenys mes recents, la xarxa dins del xip també es converteix en un coll d'ampolla que pot afectar negativament el rendiment, ja que les xarxes tradicionals poden trobar limitacions a la seva escalabilitat en el futur proper. Pràcticament la totalitat dels dissenys actuals implementen jerarquies de memòria que es comuniquen mitjançant rapides xarxes d’interconnexió. Aquesta organització es eficaç ates que permet reduir el nombre d'accessos que es realitzen a memòria principal i la latència mitjana d’accés a memòria. Les caches, la xarxa d’interconnexió i la memòria principal, conjuntament amb altres tècniques conegudes com la prebúsqueda, permeten reduir les enormes latències d’accés a memòria principal, limitant així l'impacte negatiu ocasionat per la diferencia de rendiment existent entre els nuclis de còmput i la memòria. No obstant això, compartir els recursos esmentats és font de diversos problemes i reptes, sent un dels principals la gestió de la interferència entre aplicacions. Fer un us eficient de la jerarquia de memòria i les caches, així com comptar amb una xarxa d’interconnexió apropiada, es necessari per sostenir el creixement del rendiment en els dissenys tant actuals com futurs. Aquesta tesi analitza i estudia els principals problemes i inconvenients observats en aquests dos recursos: la memòria cache d’últim nivell i la xarxa dins del xip. En primer lloc, s'estudia l'escalabilitat de les xarxes tradicionals dins del xip amb topologia de malla, així com aquesta es pot veure compromesa en propers dissenys que compten amb major nombre de nuclis. Els resultats d'aquest estudi mostren que, a major nombre de nuclis, l'impacte negatiu de la distància entre nuclis en la latència pot afectar seriosament al rendiment del processador. Com a solució' a aquest problema, en aquesta tesi proposem una xarxa d’interconnexió' òptica modelada en un entorn de simulació detallat, que suposa una solució viable als problemes d'escalabilitat observats en els dissenys tradicionals. A continuació, aquesta tesi dedica un esforç important a identificar i proposar solucions als principals problemes de disseny de les jerarquies de memòria actuals com son, per exemple, el sobredimensionat de l'espai de memòria cache privat, l’existència de repliques de dades i la rigidesa i incapacitat d’adaptació' de les estructures de memòria cache. Encara que ben coneguts, aquests problemes i els seus efectes adversos en el rendiment poden ser evitats en processadors d'alt rendiment gracies a l'enorme capacitat de la memòria cache d’últim nivell que aquest tipus de processadors típicament implementen. No obstant això, en processadors de baix consum, no hi ha la possibilitat de comptar amb aquestes capacitats, i fer un us eficient de l'espai disponible es torna crític per mantenir el rendiment. Com a solució a aquests problemes en processadors de baix consum, proposem una nova organització de jerarquia de dos nivells de memòria cache que utilitza una xarxa d’interconnexió òptica. Els resultats obtinguts mostren que, comparat amb dissenys convencionals, el consum d'energia estàtica en l'arquitectura proposada és un 60% menor, malgrat que els resultats de rendiment presenten valors similars. Per últim, hem estes l'arquitectura proposada per donar suport tant a aplicacions paral·leles com seqüencials. Els resultats obtinguts amb aquesta nova arquitectura mostren un estalvi de fins al 78 % d'energia estàtica en l’execució d'aplicacions paral·leles.[EN] Current multicores face the challenge of sharing resources among the different processor cores. Two main shared resources act as major performance bottlenecks in current designs: the off-chip main memory bandwidth and the last level cache. Additionally, as the core count grows, the network on-chip is also becoming a potential performance bottleneck, since traditional designs may find scalability issues in the near future. Memory hierarchies communicated through fast interconnects are implemented in almost every current design as they reduce the number of off-chip accesses and the overall latency, respectively. Main memory, caches, and interconnection resources, together with other widely-used techniques like prefetching, help alleviate the huge memory access latencies and limit the impact of the core-memory speed gap. However, sharing these resources brings several concerns, being one of the most challenging the management of the inter-application interference. Since almost every running application needs to access to main memory, all of them are exposed to interference from other co-runners in their way to the memory controller. For this reason, making an efficient use of the available cache space, together with achieving fast and scalable interconnects, is critical to sustain the performance in current and future designs. This dissertation analyzes and addresses the most important shortcomings of two major shared resources: the Last Level Cache (LLC) and the Network on Chip (NoC). First, we study the scalability of both electrical and optical NoCs for future multicoresand many-cores. To perform this study, we model optical interconnects in a cycle-accurate multicore simulation framework. A proper model is required; otherwise, important performance deviations may be observed otherwise in the evaluation results. The study reveals that, as the core count grows, the effect of distance on the end-to-end latency can negatively impact on the processor performance. In contrast, the study also shows that silicon nanophotonics are a viable solution to solve the mentioned latency problems. This dissertation is also motivated by important design concerns related to current memory hierarchies, like the oversizing of private cache space, data replication overheads, and lack of flexibility regarding sharing of cache structures. These issues, which can be overcome in high performance processors by virtue of huge LLCs, can compromise performance in low power processors. To address these issues we propose a more efficient cache hierarchy organization that leverages optical interconnects. The proposed architecture is conceived as an optically interconnected two-level cache hierarchy composed of multiple cache modules that can be dynamically turned on and off independently. Experimental results show that, compared to conventional designs, static energy consumption is improved by up to 60% while achieving similar performance results. Finally, we extend the proposal to support both sequential and parallel applications. This extension is required since the proposal adapts to the dynamic cache space needs of the running applications, and multithreaded applications's behaviors widely differ from those of single threaded programs. In addition, coherence management is also addressed, which is challenging since each cache module can be assigned to any core at a given time in the proposed approach. For parallel applications, the evaluation shows that the proposal achieves up to 78% static energy savings. In summary, this thesis tackles major challenges originated by the sharing of on-chip caches and communication resources in current multicores, and proposes new cache hierarchy organizations leveraging optical interconnects to address them. The proposed organizations reduce both static and dynamic energy consumption compared to conventional approaches while achieving similar performance; which results in better energy efficiency.Puche Lara, J. (2021). Novel Cache Hierarchies with Photonic Interconnects for Chip Multiprocessors [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/165254TESI

High performance computing with FPGAs

Field-programmable gate arrays represent an army of logical units which can be organized in a highly parallel or pipelined fashion to implement an algorithm in hardware. The flexibility of this new medium creates new challenges to find the right processing paradigm which takes into account of the natural constraints of FPGAs: clock frequency, memory footprint and communication bandwidth. In this paper first use of FPGAs as a multiprocessor on a chip or its use as a highly functional coprocessor are compared, and the programming tools for hardware/software codesign are discussed. Next a number of techniques are presented to maximize the parallelism and optimize the data locality in nested loops. This includes unimodular transformations, data locality improving loop transformations and use of smart buffers. Finally, the use of these techniques on a number of examples is demonstrated. The results in the paper and in the literature show that, with the proper programming tool set, FPGAs can speedup computation kernels significantly with respect to traditional processors